LMFDB - Embedded newform 1334.2.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$10.6520436296$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5x^{9} - 8x^{8} + 60x^{7} + 13x^{6} - 241x^{5} + 6x^{4} + 346x^{3} + 16x^{2} - 64x - 12 $ x^10 - 5x^9 - 8x^8 + 60x^7 + 13x^6 - 241x^5 + 6x^4 + 346x^3 + 16x^2 - 64*x - 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.05371$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.05371 q^{3} +1.00000 q^{4} -4.01245 q^{5} -2.05371 q^{6} -3.53542 q^{7} +1.00000 q^{8} +1.21772 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.05371 q^{3} +1.00000 q^{4} -4.01245 q^{5} -2.05371 q^{6} -3.53542 q^{7} +1.00000 q^{8} +1.21772 q^{9} -4.01245 q^{10} -5.51177 q^{11} -2.05371 q^{12} +0.652850 q^{13} -3.53542 q^{14} +8.24041 q^{15} +1.00000 q^{16} -1.70048 q^{17} +1.21772 q^{18} +3.73557 q^{19} -4.01245 q^{20} +7.26073 q^{21} -5.51177 q^{22} +1.00000 q^{23} -2.05371 q^{24} +11.0998 q^{25} +0.652850 q^{26} +3.66028 q^{27} -3.53542 q^{28} +1.00000 q^{29} +8.24041 q^{30} +10.0628 q^{31} +1.00000 q^{32} +11.3196 q^{33} -1.70048 q^{34} +14.1857 q^{35} +1.21772 q^{36} -6.14105 q^{37} +3.73557 q^{38} -1.34076 q^{39} -4.01245 q^{40} -11.4023 q^{41} +7.26073 q^{42} -8.03976 q^{43} -5.51177 q^{44} -4.88605 q^{45} +1.00000 q^{46} +1.42410 q^{47} -2.05371 q^{48} +5.49923 q^{49} +11.0998 q^{50} +3.49230 q^{51} +0.652850 q^{52} -13.4566 q^{53} +3.66028 q^{54} +22.1157 q^{55} -3.53542 q^{56} -7.67177 q^{57} +1.00000 q^{58} +10.6151 q^{59} +8.24041 q^{60} -1.51568 q^{61} +10.0628 q^{62} -4.30516 q^{63} +1.00000 q^{64} -2.61953 q^{65} +11.3196 q^{66} +6.39521 q^{67} -1.70048 q^{68} -2.05371 q^{69} +14.1857 q^{70} -5.18060 q^{71} +1.21772 q^{72} -0.504417 q^{73} -6.14105 q^{74} -22.7957 q^{75} +3.73557 q^{76} +19.4865 q^{77} -1.34076 q^{78} +6.23760 q^{79} -4.01245 q^{80} -11.1703 q^{81} -11.4023 q^{82} +0.224971 q^{83} +7.26073 q^{84} +6.82311 q^{85} -8.03976 q^{86} -2.05371 q^{87} -5.51177 q^{88} +11.8609 q^{89} -4.88605 q^{90} -2.30810 q^{91} +1.00000 q^{92} -20.6661 q^{93} +1.42410 q^{94} -14.9888 q^{95} -2.05371 q^{96} +6.01214 q^{97} +5.49923 q^{98} -6.71180 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9} - q^{10} + q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 10 q^{16} + 11 q^{18} + 20 q^{19} - q^{20} + 14 q^{21} + q^{22} + 10 q^{23} + 5 q^{24} + 23 q^{25} + 9 q^{26} + 23 q^{27} + 2 q^{28} + 10 q^{29} + 5 q^{30} + 21 q^{31} + 10 q^{32} + q^{33} + 2 q^{35} + 11 q^{36} - 8 q^{37} + 20 q^{38} + 23 q^{39} - q^{40} - 4 q^{41} + 14 q^{42} - 3 q^{43} + q^{44} - 18 q^{45} + 10 q^{46} - q^{47} + 5 q^{48} + 18 q^{49} + 23 q^{50} - 6 q^{51} + 9 q^{52} - 13 q^{53} + 23 q^{54} + 13 q^{55} + 2 q^{56} - 22 q^{57} + 10 q^{58} + 14 q^{59} + 5 q^{60} + 12 q^{61} + 21 q^{62} - 26 q^{63} + 10 q^{64} - 25 q^{65} + q^{66} + 6 q^{67} + 5 q^{69} + 2 q^{70} + 8 q^{71} + 11 q^{72} + 16 q^{73} - 8 q^{74} + 8 q^{75} + 20 q^{76} - 16 q^{77} + 23 q^{78} + 7 q^{79} - q^{80} - 2 q^{81} - 4 q^{82} + 18 q^{83} + 14 q^{84} + 8 q^{85} - 3 q^{86} + 5 q^{87} + q^{88} + 2 q^{89} - 18 q^{90} + 8 q^{91} + 10 q^{92} - 41 q^{93} - q^{94} - 16 q^{95} + 5 q^{96} + 6 q^{97} + 18 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9 - q^10 + q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 10 * q^16 + 11 * q^18 + 20 * q^19 - q^20 + 14 * q^21 + q^22 + 10 * q^23 + 5 * q^24 + 23 * q^25 + 9 * q^26 + 23 * q^27 + 2 * q^28 + 10 * q^29 + 5 * q^30 + 21 * q^31 + 10 * q^32 + q^33 + 2 * q^35 + 11 * q^36 - 8 * q^37 + 20 * q^38 + 23 * q^39 - q^40 - 4 * q^41 + 14 * q^42 - 3 * q^43 + q^44 - 18 * q^45 + 10 * q^46 - q^47 + 5 * q^48 + 18 * q^49 + 23 * q^50 - 6 * q^51 + 9 * q^52 - 13 * q^53 + 23 * q^54 + 13 * q^55 + 2 * q^56 - 22 * q^57 + 10 * q^58 + 14 * q^59 + 5 * q^60 + 12 * q^61 + 21 * q^62 - 26 * q^63 + 10 * q^64 - 25 * q^65 + q^66 + 6 * q^67 + 5 * q^69 + 2 * q^70 + 8 * q^71 + 11 * q^72 + 16 * q^73 - 8 * q^74 + 8 * q^75 + 20 * q^76 - 16 * q^77 + 23 * q^78 + 7 * q^79 - q^80 - 2 * q^81 - 4 * q^82 + 18 * q^83 + 14 * q^84 + 8 * q^85 - 3 * q^86 + 5 * q^87 + q^88 + 2 * q^89 - 18 * q^90 + 8 * q^91 + 10 * q^92 - 41 * q^93 - q^94 - 16 * q^95 + 5 * q^96 + 6 * q^97 + 18 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.05371	−1.18571	−0.592855	−	0.805309i	$-0.701999\pi$
$3$	−2.05371	−1.18571	−0.592855	+	0.805309i	$0.701999\pi$
$4$	1.00000	0.500000
$5$	−4.01245	−1.79442	−0.897212	−	0.441600i	$-0.854411\pi$
$5$	−4.01245	−1.79442	−0.897212	+	0.441600i	$0.854411\pi$
$6$	−2.05371	−0.838423
$7$	−3.53542	−1.33626	−0.668132	−	0.744042i	$-0.732906\pi$
$7$	−3.53542	−1.33626	−0.668132	+	0.744042i	$0.732906\pi$
$8$	1.00000	0.353553
$9$	1.21772	0.405907
$10$	−4.01245	−1.26885
$11$	−5.51177	−1.66186	−0.830931	−	0.556375i	$-0.812192\pi$
$11$	−5.51177	−1.66186	−0.830931	+	0.556375i	$0.812192\pi$
$12$	−2.05371	−0.592855
$13$	0.652850	0.181068	0.0905340	−	0.995893i	$-0.471143\pi$
$13$	0.652850	0.181068	0.0905340	+	0.995893i	$0.471143\pi$
$14$	−3.53542	−0.944882
$15$	8.24041	2.12767
$16$	1.00000	0.250000
$17$	−1.70048	−0.412428	−0.206214	−	0.978507i	$-0.566114\pi$
$17$	−1.70048	−0.412428	−0.206214	+	0.978507i	$0.566114\pi$
$18$	1.21772	0.287019
$19$	3.73557	0.856998	0.428499	−	0.903542i	$-0.359042\pi$
$19$	3.73557	0.856998	0.428499	+	0.903542i	$0.359042\pi$
$20$	−4.01245	−0.897212
$21$	7.26073	1.58442
$22$	−5.51177	−1.17511
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.05371	−0.419212
$25$	11.0998	2.21996
$26$	0.652850	0.128034
$27$	3.66028	0.704422
$28$	−3.53542	−0.668132
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	8.24041	1.50449
$31$	10.0628	1.80733	0.903666	−	0.428238i	$-0.140866\pi$
$31$	10.0628	1.80733	0.903666	+	0.428238i	$0.140866\pi$
$32$	1.00000	0.176777
$33$	11.3196	1.97049
$34$	−1.70048	−0.291630
$35$	14.1857	2.39783
$36$	1.21772	0.202953
$37$	−6.14105	−1.00958	−0.504791	−	0.863242i	$-0.668430\pi$
$37$	−6.14105	−1.00958	−0.504791	+	0.863242i	$0.668430\pi$
$38$	3.73557	0.605989
$39$	−1.34076	−0.214694
$40$	−4.01245	−0.634425
$41$	−11.4023	−1.78074	−0.890372	−	0.455234i	$-0.849556\pi$
$41$	−11.4023	−1.78074	−0.890372	+	0.455234i	$0.849556\pi$
$42$	7.26073	1.12036
$43$	−8.03976	−1.22605	−0.613026	−	0.790062i	$-0.710048\pi$
$43$	−8.03976	−1.22605	−0.613026	+	0.790062i	$0.710048\pi$
$44$	−5.51177	−0.830931
$45$	−4.88605	−0.728369
$46$	1.00000	0.147442
$47$	1.42410	0.207726	0.103863	−	0.994592i	$-0.466880\pi$
$47$	1.42410	0.207726	0.103863	+	0.994592i	$0.466880\pi$
$48$	−2.05371	−0.296427
$49$	5.49923	0.785604
$50$	11.0998	1.56975
$51$	3.49230	0.489019
$52$	0.652850	0.0905340
$53$	−13.4566	−1.84840	−0.924201	−	0.381906i	$-0.875268\pi$
$53$	−13.4566	−1.84840	−0.924201	+	0.381906i	$0.875268\pi$
$54$	3.66028	0.498102
$55$	22.1157	2.98209
$56$	−3.53542	−0.472441
$57$	−7.67177	−1.01615
$58$	1.00000	0.131306
$59$	10.6151	1.38197	0.690984	−	0.722870i	$-0.257178\pi$
$59$	10.6151	1.38197	0.690984	+	0.722870i	$0.257178\pi$
$60$	8.24041	1.06383
$61$	−1.51568	−0.194063	−0.0970315	−	0.995281i	$-0.530935\pi$
$61$	−1.51568	−0.194063	−0.0970315	+	0.995281i	$0.530935\pi$
$62$	10.0628	1.27798
$63$	−4.30516	−0.542399
$64$	1.00000	0.125000
$65$	−2.61953	−0.324913
$66$	11.3196	1.39334
$67$	6.39521	0.781299	0.390650	−	0.920539i	$-0.372250\pi$
$67$	6.39521	0.781299	0.390650	+	0.920539i	$0.372250\pi$
$68$	−1.70048	−0.206214
$69$	−2.05371	−0.247238
$70$	14.1857	1.69552
$71$	−5.18060	−0.614824	−0.307412	−	0.951576i	$-0.599463\pi$
$71$	−5.18060	−0.614824	−0.307412	+	0.951576i	$0.599463\pi$
$72$	1.21772	0.143510
$73$	−0.504417	−0.0590375	−0.0295187	−	0.999564i	$-0.509397\pi$
$73$	−0.504417	−0.0590375	−0.0295187	+	0.999564i	$0.509397\pi$
$74$	−6.14105	−0.713882
$75$	−22.7957	−2.63222
$76$	3.73557	0.428499
$77$	19.4865	2.22069
$78$	−1.34076	−0.151812
$79$	6.23760	0.701785	0.350892	−	0.936416i	$-0.385878\pi$
$79$	6.23760	0.701785	0.350892	+	0.936416i	$0.385878\pi$
$80$	−4.01245	−0.448606
$81$	−11.1703	−1.24115
$82$	−11.4023	−1.25918
$83$	0.224971	0.0246938	0.0123469	−	0.999924i	$-0.496070\pi$
$83$	0.224971	0.0246938	0.0123469	+	0.999924i	$0.496070\pi$
$84$	7.26073	0.792211
$85$	6.82311	0.740070
$86$	−8.03976	−0.866950
$87$	−2.05371	−0.220181
$88$	−5.51177	−0.587557
$89$	11.8609	1.25725	0.628625	−	0.777709i	$-0.283618\pi$
$89$	11.8609	1.25725	0.628625	+	0.777709i	$0.283618\pi$
$90$	−4.88605	−0.515035
$91$	−2.30810	−0.241955
$92$	1.00000	0.104257
$93$	−20.6661	−2.14297
$94$	1.42410	0.146885
$95$	−14.9888	−1.53782
$96$	−2.05371	−0.209606
$97$	6.01214	0.610441	0.305220	−	0.952282i	$-0.401270\pi$
$97$	6.01214	0.610441	0.305220	+	0.952282i	$0.401270\pi$
$98$	5.49923	0.555506
$99$	−6.71180	−0.674561
$100$	11.0998	1.10998
$101$	−0.551787	−0.0549048	−0.0274524	−	0.999623i	$-0.508739\pi$
$101$	−0.551787	−0.0549048	−0.0274524	+	0.999623i	$0.508739\pi$
$102$	3.49230	0.345789
$103$	1.20618	0.118849	0.0594243	−	0.998233i	$-0.481073\pi$
$103$	1.20618	0.118849	0.0594243	+	0.998233i	$0.481073\pi$
$104$	0.652850	0.0640172
$105$	−29.1334	−2.84312
$106$	−13.4566	−1.30702
$107$	1.87585	0.181346	0.0906729	−	0.995881i	$-0.471098\pi$
$107$	1.87585	0.181346	0.0906729	+	0.995881i	$0.471098\pi$
$108$	3.66028	0.352211
$109$	9.73315	0.932267	0.466134	−	0.884714i	$-0.345647\pi$
$109$	9.73315	0.932267	0.466134	+	0.884714i	$0.345647\pi$
$110$	22.1157	2.10865
$111$	12.6119	1.19707
$112$	−3.53542	−0.334066
$113$	11.2161	1.05512	0.527562	−	0.849516i	$-0.323106\pi$
$113$	11.2161	1.05512	0.527562	+	0.849516i	$0.323106\pi$
$114$	−7.67177	−0.718527
$115$	−4.01245	−0.374163
$116$	1.00000	0.0928477
$117$	0.794989	0.0734967
$118$	10.6151	0.977199
$119$	6.01193	0.551113
$120$	8.24041	0.752243
$121$	19.3797	1.76179
$122$	−1.51568	−0.137223
$123$	23.4171	2.11144
$124$	10.0628	0.903666
$125$	−24.4751	−2.18912
$126$	−4.30516	−0.383534
$127$	−17.9486	−1.59268	−0.796339	−	0.604850i	$-0.793233\pi$
$127$	−17.9486	−1.59268	−0.796339	+	0.604850i	$0.793233\pi$
$128$	1.00000	0.0883883
$129$	16.5113	1.45374
$130$	−2.61953	−0.229748
$131$	−12.9396	−1.13054	−0.565271	−	0.824905i	$-0.691228\pi$
$131$	−12.9396	−1.13054	−0.565271	+	0.824905i	$0.691228\pi$
$132$	11.3196	0.985243
$133$	−13.2068	−1.14518
$134$	6.39521	0.552462
$135$	−14.6867	−1.26403
$136$	−1.70048	−0.145815
$137$	7.26481	0.620675	0.310337	−	0.950626i	$-0.399558\pi$
$137$	7.26481	0.620675	0.310337	+	0.950626i	$0.399558\pi$
$138$	−2.05371	−0.174823
$139$	−5.41103	−0.458957	−0.229479	−	0.973314i	$-0.573702\pi$
$139$	−5.41103	−0.458957	−0.229479	+	0.973314i	$0.573702\pi$
$140$	14.1857	1.19891
$141$	−2.92469	−0.246303
$142$	−5.18060	−0.434746
$143$	−3.59836	−0.300910
$144$	1.21772	0.101477
$145$	−4.01245	−0.333216
$146$	−0.504417	−0.0417458
$147$	−11.2938	−0.931498
$148$	−6.14105	−0.504791
$149$	−16.2539	−1.33158	−0.665788	−	0.746141i	$-0.731904\pi$
$149$	−16.2539	−1.33158	−0.665788	+	0.746141i	$0.731904\pi$
$150$	−22.7957	−1.86126
$151$	8.56052	0.696645	0.348323	−	0.937375i	$-0.386751\pi$
$151$	8.56052	0.696645	0.348323	+	0.937375i	$0.386751\pi$
$152$	3.73557	0.302995
$153$	−2.07071	−0.167407
$154$	19.4865	1.57026
$155$	−40.3765	−3.24312
$156$	−1.34076	−0.107347
$157$	9.66034	0.770979	0.385490	−	0.922712i	$-0.374033\pi$
$157$	9.66034	0.770979	0.385490	+	0.922712i	$0.374033\pi$
$158$	6.23760	0.496237
$159$	27.6359	2.19167
$160$	−4.01245	−0.317212
$161$	−3.53542	−0.278631
$162$	−11.1703	−0.877623
$163$	−11.9648	−0.937155	−0.468577	−	0.883422i	$-0.655233\pi$
$163$	−11.9648	−0.937155	−0.468577	+	0.883422i	$0.655233\pi$
$164$	−11.4023	−0.890372
$165$	−45.4193	−3.53589
$166$	0.224971	0.0174611
$167$	25.2108	1.95087	0.975435	−	0.220288i	$-0.0706997\pi$
$167$	25.2108	1.95087	0.975435	+	0.220288i	$0.0706997\pi$
$168$	7.26073	0.560178
$169$	−12.5738	−0.967214
$170$	6.82311	0.523308
$171$	4.54888	0.347862
$172$	−8.03976	−0.613026
$173$	9.32871	0.709248	0.354624	−	0.935009i	$-0.384609\pi$
$173$	9.32871	0.709248	0.354624	+	0.935009i	$0.384609\pi$
$174$	−2.05371	−0.155691
$175$	−39.2425	−2.96645
$176$	−5.51177	−0.415466
$177$	−21.8003	−1.63861
$178$	11.8609	0.889009
$179$	16.2299	1.21308	0.606540	−	0.795053i	$-0.292557\pi$
$179$	16.2299	1.21308	0.606540	+	0.795053i	$0.292557\pi$
$180$	−4.88605	−0.364184
$181$	−14.1741	−1.05355	−0.526777	−	0.850003i	$-0.676600\pi$
$181$	−14.1741	−1.05355	−0.526777	+	0.850003i	$0.676600\pi$
$182$	−2.30810	−0.171088
$183$	3.11277	0.230102
$184$	1.00000	0.0737210
$185$	24.6407	1.81162
$186$	−20.6661	−1.51531
$187$	9.37268	0.685398
$188$	1.42410	0.103863
$189$	−12.9407	−0.941294
$190$	−14.9888	−1.08740
$191$	25.6398	1.85523	0.927614	−	0.373541i	$-0.121856\pi$
$191$	25.6398	1.85523	0.927614	+	0.373541i	$0.121856\pi$
$192$	−2.05371	−0.148214
$193$	11.6598	0.839291	0.419645	−	0.907688i	$-0.362154\pi$
$193$	11.6598	0.839291	0.419645	+	0.907688i	$0.362154\pi$
$194$	6.01214	0.431647
$195$	5.37975	0.385252
$196$	5.49923	0.392802
$197$	−9.64941	−0.687492	−0.343746	−	0.939063i	$-0.611696\pi$
$197$	−9.64941	−0.687492	−0.343746	+	0.939063i	$0.611696\pi$
$198$	−6.71180	−0.476987
$199$	−1.69254	−0.119981	−0.0599907	−	0.998199i	$-0.519107\pi$
$199$	−1.69254	−0.119981	−0.0599907	+	0.998199i	$0.519107\pi$
$200$	11.0998	0.784873
$201$	−13.1339	−0.926394
$202$	−0.551787	−0.0388236
$203$	−3.53542	−0.248138
$204$	3.49230	0.244510
$205$	45.7513	3.19541
$206$	1.20618	0.0840387
$207$	1.21772	0.0846374
$208$	0.652850	0.0452670
$209$	−20.5896	−1.42421
$210$	−29.1334	−2.01039
$211$	13.0577	0.898927	0.449464	−	0.893299i	$-0.351615\pi$
$211$	13.0577	0.898927	0.449464	+	0.893299i	$0.351615\pi$
$212$	−13.4566	−0.924201
$213$	10.6394	0.729003
$214$	1.87585	0.128231
$215$	32.2592	2.20006
$216$	3.66028	0.249051
$217$	−35.5763	−2.41507
$218$	9.73315	0.659212
$219$	1.03592	0.0700013
$220$	22.1157	1.49104
$221$	−1.11016	−0.0746774
$222$	12.6119	0.846457
$223$	−0.650247	−0.0435438	−0.0217719	−	0.999763i	$-0.506931\pi$
$223$	−0.650247	−0.0435438	−0.0217719	+	0.999763i	$0.506931\pi$
$224$	−3.53542	−0.236221
$225$	13.5164	0.901096
$226$	11.2161	0.746086
$227$	−1.23447	−0.0819344	−0.0409672	−	0.999160i	$-0.513044\pi$
$227$	−1.23447	−0.0819344	−0.0409672	+	0.999160i	$0.513044\pi$
$228$	−7.67177	−0.508076
$229$	−14.4713	−0.956292	−0.478146	−	0.878280i	$-0.658691\pi$
$229$	−14.4713	−0.956292	−0.478146	+	0.878280i	$0.658691\pi$
$230$	−4.01245	−0.264573
$231$	−40.0195	−2.63309
$232$	1.00000	0.0656532
$233$	−27.8455	−1.82422	−0.912110	−	0.409945i	$-0.865548\pi$
$233$	−27.8455	−1.82422	−0.912110	+	0.409945i	$0.865548\pi$
$234$	0.794989	0.0519700
$235$	−5.71414	−0.372749
$236$	10.6151	0.690984
$237$	−12.8102	−0.832113
$238$	6.01193	0.389695
$239$	−10.6587	−0.689452	−0.344726	−	0.938703i	$-0.612028\pi$
$239$	−10.6587	−0.689452	−0.344726	+	0.938703i	$0.612028\pi$
$240$	8.24041	0.531916
$241$	21.0409	1.35537	0.677683	−	0.735354i	$-0.262984\pi$
$241$	21.0409	1.35537	0.677683	+	0.735354i	$0.262984\pi$
$242$	19.3797	1.24577
$243$	11.9597	0.767217
$244$	−1.51568	−0.0970315
$245$	−22.0654	−1.40971
$246$	23.4171	1.49302
$247$	2.43877	0.155175
$248$	10.0628	0.638988
$249$	−0.462025	−0.0292796
$250$	−24.4751	−1.54794
$251$	18.0464	1.13908	0.569540	−	0.821964i	$-0.307121\pi$
$251$	18.0464	1.13908	0.569540	+	0.821964i	$0.307121\pi$
$252$	−4.30516	−0.271200
$253$	−5.51177	−0.346522
$254$	−17.9486	−1.12619
$255$	−14.0127	−0.877508
$256$	1.00000	0.0625000
$257$	−23.2017	−1.44728	−0.723642	−	0.690175i	$-0.757533\pi$
$257$	−23.2017	−1.44728	−0.723642	+	0.690175i	$0.757533\pi$
$258$	16.5113	1.02795
$259$	21.7112	1.34907
$260$	−2.61953	−0.162456
$261$	1.21772	0.0753750
$262$	−12.9396	−0.799414
$263$	7.85841	0.484570	0.242285	−	0.970205i	$-0.422103\pi$
$263$	7.85841	0.484570	0.242285	+	0.970205i	$0.422103\pi$
$264$	11.3196	0.696672
$265$	53.9939	3.31682
$266$	−13.2068	−0.809762
$267$	−24.3588	−1.49073
$268$	6.39521	0.390650
$269$	−0.813498	−0.0495999	−0.0247999	−	0.999692i	$-0.507895\pi$
$269$	−0.813498	−0.0495999	−0.0247999	+	0.999692i	$0.507895\pi$
$270$	−14.6867	−0.893805
$271$	22.4466	1.36354	0.681768	−	0.731568i	$-0.261211\pi$
$271$	22.4466	1.36354	0.681768	+	0.731568i	$0.261211\pi$
$272$	−1.70048	−0.103107
$273$	4.74017	0.286888
$274$	7.26481	0.438883
$275$	−61.1795	−3.68926
$276$	−2.05371	−0.123619
$277$	12.6782	0.761759	0.380879	−	0.924625i	$-0.375621\pi$
$277$	12.6782	0.761759	0.380879	+	0.924625i	$0.375621\pi$
$278$	−5.41103	−0.324532
$279$	12.2537	0.733608
$280$	14.1857	0.847759
$281$	16.9169	1.00918	0.504590	−	0.863359i	$-0.331644\pi$
$281$	16.9169	1.00918	0.504590	+	0.863359i	$0.331644\pi$
$282$	−2.92469	−0.174163
$283$	31.0461	1.84550	0.922749	−	0.385401i	$-0.125937\pi$
$283$	31.0461	1.84550	0.922749	+	0.385401i	$0.125937\pi$
$284$	−5.18060	−0.307412
$285$	30.7826	1.82341
$286$	−3.59836	−0.212776
$287$	40.3121	2.37955
$288$	1.21772	0.0717549
$289$	−14.1084	−0.829903
$290$	−4.01245	−0.235619
$291$	−12.3472	−0.723805
$292$	−0.504417	−0.0295187
$293$	0.204091	0.0119231	0.00596155	−	0.999982i	$-0.498102\pi$
$293$	0.204091	0.0119231	0.00596155	+	0.999982i	$0.498102\pi$
$294$	−11.2938	−0.658669
$295$	−42.5926	−2.47984
$296$	−6.14105	−0.356941
$297$	−20.1747	−1.17065
$298$	−16.2539	−0.941566
$299$	0.652850	0.0377553
$300$	−22.7957	−1.31611
$301$	28.4240	1.63833
$302$	8.56052	0.492602
$303$	1.13321	0.0651012
$304$	3.73557	0.214250
$305$	6.08160	0.348231
$306$	−2.07071	−0.118375
$307$	−18.6866	−1.06650	−0.533249	−	0.845958i	$-0.679029\pi$
$307$	−18.6866	−1.06650	−0.533249	+	0.845958i	$0.679029\pi$
$308$	19.4865	1.11034
$309$	−2.47715	−0.140920
$310$	−40.3765	−2.29323
$311$	−12.9694	−0.735429	−0.367715	−	0.929939i	$-0.619860\pi$
$311$	−12.9694	−0.735429	−0.367715	+	0.929939i	$0.619860\pi$
$312$	−1.34076	−0.0759058
$313$	6.21956	0.351550	0.175775	−	0.984430i	$-0.443757\pi$
$313$	6.21956	0.351550	0.175775	+	0.984430i	$0.443757\pi$
$314$	9.66034	0.545165
$315$	17.2742	0.973294
$316$	6.23760	0.350892
$317$	2.43300	0.136651	0.0683254	−	0.997663i	$-0.478234\pi$
$317$	2.43300	0.136651	0.0683254	+	0.997663i	$0.478234\pi$
$318$	27.6359	1.54974
$319$	−5.51177	−0.308600
$320$	−4.01245	−0.224303
$321$	−3.85246	−0.215023
$322$	−3.53542	−0.197022
$323$	−6.35227	−0.353450
$324$	−11.1703	−0.620573
$325$	7.24649	0.401963
$326$	−11.9648	−0.662669
$327$	−19.9891	−1.10540
$328$	−11.4023	−0.629588
$329$	−5.03480	−0.277578
$330$	−45.4193	−2.50025
$331$	3.43227	0.188655	0.0943274	−	0.995541i	$-0.469930\pi$
$331$	3.43227	0.188655	0.0943274	+	0.995541i	$0.469930\pi$
$332$	0.224971	0.0123469
$333$	−7.47808	−0.409796
$334$	25.2108	1.37947
$335$	−25.6605	−1.40198
$336$	7.26073	0.396105
$337$	−26.7191	−1.45548	−0.727741	−	0.685852i	$-0.759430\pi$
$337$	−26.7191	−1.45548	−0.727741	+	0.685852i	$0.759430\pi$
$338$	−12.5738	−0.683924
$339$	−23.0347	−1.25107
$340$	6.82311	0.370035
$341$	−55.4639	−3.00354
$342$	4.54888	0.245975
$343$	5.30587	0.286490
$344$	−8.03976	−0.433475
$345$	8.24041	0.443649
$346$	9.32871	0.501514
$347$	−8.08819	−0.434197	−0.217098	−	0.976150i	$-0.569659\pi$
$347$	−8.08819	−0.434197	−0.217098	+	0.976150i	$0.569659\pi$
$348$	−2.05371	−0.110090
$349$	19.0010	1.01710	0.508550	−	0.861032i	$-0.330182\pi$
$349$	19.0010	1.01710	0.508550	+	0.861032i	$0.330182\pi$
$350$	−39.2425	−2.09760
$351$	2.38962	0.127548
$352$	−5.51177	−0.293779
$353$	25.7234	1.36912	0.684561	−	0.728956i	$-0.259994\pi$
$353$	25.7234	1.36912	0.684561	+	0.728956i	$0.259994\pi$
$354$	−21.8003	−1.15867
$355$	20.7869	1.10326
$356$	11.8609	0.628625
$357$	−12.3468	−0.653459
$358$	16.2299	0.857778
$359$	−0.524332	−0.0276732	−0.0138366	−	0.999904i	$-0.504404\pi$
$359$	−0.524332	−0.0276732	−0.0138366	+	0.999904i	$0.504404\pi$
$360$	−4.88605	−0.257517
$361$	−5.04552	−0.265554
$362$	−14.1741	−0.744975
$363$	−39.8002	−2.08897
$364$	−2.30810	−0.120977
$365$	2.02395	0.105938
$366$	3.11277	0.162707
$367$	30.2026	1.57656	0.788282	−	0.615314i	$-0.210971\pi$
$367$	30.2026	1.57656	0.788282	+	0.615314i	$0.210971\pi$
$368$	1.00000	0.0521286
$369$	−13.8848	−0.722816
$370$	24.6407	1.28101
$371$	47.5747	2.46996
$372$	−20.6661	−1.07149
$373$	−13.8974	−0.719582	−0.359791	−	0.933033i	$-0.617152\pi$
$373$	−13.8974	−0.719582	−0.359791	+	0.933033i	$0.617152\pi$
$374$	9.37268	0.484650
$375$	50.2647	2.59566
$376$	1.42410	0.0734424
$377$	0.652850	0.0336235
$378$	−12.9407	−0.665596
$379$	−6.36361	−0.326877	−0.163438	−	0.986554i	$-0.552259\pi$
$379$	−6.36361	−0.326877	−0.163438	+	0.986554i	$0.552259\pi$
$380$	−14.9888	−0.768909
$381$	36.8612	1.88845
$382$	25.6398	1.31184
$383$	−1.24342	−0.0635359	−0.0317679	−	0.999495i	$-0.510114\pi$
$383$	−1.24342	−0.0635359	−0.0317679	+	0.999495i	$0.510114\pi$
$384$	−2.05371	−0.104803
$385$	−78.1885	−3.98486
$386$	11.6598	0.593468
$387$	−9.79019	−0.497663
$388$	6.01214	0.305220
$389$	−21.6016	−1.09525	−0.547623	−	0.836725i	$-0.684467\pi$
$389$	−21.6016	−1.09525	−0.547623	+	0.836725i	$0.684467\pi$
$390$	5.37975	0.272414
$391$	−1.70048	−0.0859971
$392$	5.49923	0.277753
$393$	26.5743	1.34049
$394$	−9.64941	−0.486130
$395$	−25.0281	−1.25930
$396$	−6.71180	−0.337281
$397$	−32.1432	−1.61322	−0.806611	−	0.591083i	$-0.798700\pi$
$397$	−32.1432	−1.61322	−0.806611	+	0.591083i	$0.798700\pi$
$398$	−1.69254	−0.0848396
$399$	27.1230	1.35785
$400$	11.0998	0.554989
$401$	−7.66396	−0.382720	−0.191360	−	0.981520i	$-0.561290\pi$
$401$	−7.66396	−0.382720	−0.191360	+	0.981520i	$0.561290\pi$
$402$	−13.1339	−0.655059
$403$	6.56950	0.327250
$404$	−0.551787	−0.0274524
$405$	44.8204	2.22714
$406$	−3.53542	−0.175460
$407$	33.8481	1.67779
$408$	3.49230	0.172894
$409$	39.2906	1.94280	0.971398	−	0.237457i	$-0.0763140\pi$
$409$	39.2906	1.94280	0.971398	+	0.237457i	$0.0763140\pi$
$410$	45.7513	2.25950
$411$	−14.9198	−0.735940
$412$	1.20618	0.0594243
$413$	−37.5289	−1.84667
$414$	1.21772	0.0598477
$415$	−0.902686	−0.0443111
$416$	0.652850	0.0320086
$417$	11.1127	0.544190
$418$	−20.5896	−1.00707
$419$	12.9800	0.634113	0.317056	−	0.948407i	$-0.397306\pi$
$419$	12.9800	0.634113	0.317056	+	0.948407i	$0.397306\pi$
$420$	−29.1334	−1.42156
$421$	−1.36101	−0.0663313	−0.0331657	−	0.999450i	$-0.510559\pi$
$421$	−1.36101	−0.0663313	−0.0331657	+	0.999450i	$0.510559\pi$
$422$	13.0577	0.635638
$423$	1.73416	0.0843176
$424$	−13.4566	−0.653509
$425$	−18.8750	−0.915572
$426$	10.6394	0.515483
$427$	5.35857	0.259320
$428$	1.87585	0.0906729
$429$	7.38999	0.356792
$430$	32.2592	1.55568
$431$	14.9961	0.722334	0.361167	−	0.932501i	$-0.382378\pi$
$431$	14.9961	0.722334	0.361167	+	0.932501i	$0.382378\pi$
$432$	3.66028	0.176105
$433$	35.9301	1.72669	0.863345	−	0.504613i	$-0.168365\pi$
$433$	35.9301	1.72669	0.863345	+	0.504613i	$0.168365\pi$
$434$	−35.5763	−1.70772
$435$	8.24041	0.395098
$436$	9.73315	0.466134
$437$	3.73557	0.178697
$438$	1.03592	0.0494984
$439$	−8.90014	−0.424780	−0.212390	−	0.977185i	$-0.568125\pi$
$439$	−8.90014	−0.424780	−0.212390	+	0.977185i	$0.568125\pi$
$440$	22.1157	1.05433
$441$	6.69652	0.318882
$442$	−1.11016	−0.0528049
$443$	2.51759	0.119614	0.0598071	−	0.998210i	$-0.480951\pi$
$443$	2.51759	0.119614	0.0598071	+	0.998210i	$0.480951\pi$
$444$	12.6119	0.598536
$445$	−47.5912	−2.25604
$446$	−0.650247	−0.0307901
$447$	33.3809	1.57886
$448$	−3.53542	−0.167033
$449$	31.2412	1.47436	0.737182	−	0.675694i	$-0.236156\pi$
$449$	31.2412	1.47436	0.737182	+	0.675694i	$0.236156\pi$
$450$	13.5164	0.637171
$451$	62.8470	2.95935
$452$	11.2161	0.527562
$453$	−17.5808	−0.826019
$454$	−1.23447	−0.0579363
$455$	9.26115	0.434169
$456$	−7.67177	−0.359264
$457$	38.7886	1.81446	0.907228	−	0.420639i	$-0.138194\pi$
$457$	38.7886	1.81446	0.907228	+	0.420639i	$0.138194\pi$
$458$	−14.4713	−0.676201
$459$	−6.22425	−0.290523
$460$	−4.01245	−0.187082
$461$	−24.5073	−1.14142	−0.570710	−	0.821152i	$-0.693332\pi$
$461$	−24.5073	−1.14142	−0.570710	+	0.821152i	$0.693332\pi$
$462$	−40.0195	−1.86188
$463$	−39.1005	−1.81716	−0.908578	−	0.417715i	$-0.862831\pi$
$463$	−39.1005	−1.81716	−0.908578	+	0.417715i	$0.862831\pi$
$464$	1.00000	0.0464238
$465$	82.9216	3.84540
$466$	−27.8455	−1.28992
$467$	−18.9638	−0.877539	−0.438770	−	0.898600i	$-0.644586\pi$
$467$	−18.9638	−0.877539	−0.438770	+	0.898600i	$0.644586\pi$
$468$	0.794989	0.0367484
$469$	−22.6098	−1.04402
$470$	−5.71414	−0.263574
$471$	−19.8395	−0.914157
$472$	10.6151	0.488599
$473$	44.3134	2.03753
$474$	−12.8102	−0.588393
$475$	41.4640	1.90250
$476$	6.01193	0.275556
$477$	−16.3863	−0.750279
$478$	−10.6587	−0.487517
$479$	2.26922	0.103683	0.0518417	−	0.998655i	$-0.483491\pi$
$479$	2.26922	0.103683	0.0518417	+	0.998655i	$0.483491\pi$
$480$	8.24041	0.376122
$481$	−4.00918	−0.182803
$482$	21.0409	0.958389
$483$	7.26073	0.330375
$484$	19.3797	0.880893
$485$	−24.1235	−1.09539
$486$	11.9597	0.542504
$487$	−32.2461	−1.46121	−0.730605	−	0.682801i	$-0.760762\pi$
$487$	−32.2461	−1.46121	−0.730605	+	0.682801i	$0.760762\pi$
$488$	−1.51568	−0.0686116
$489$	24.5722	1.11119
$490$	−22.0654	−0.996813
$491$	23.7963	1.07391	0.536957	−	0.843610i	$-0.319574\pi$
$491$	23.7963	1.07391	0.536957	+	0.843610i	$0.319574\pi$
$492$	23.4171	1.05572
$493$	−1.70048	−0.0765859
$494$	2.43877	0.109725
$495$	26.9308	1.21045
$496$	10.0628	0.451833
$497$	18.3156	0.821568
$498$	−0.462025	−0.0207038
$499$	11.5684	0.517871	0.258936	−	0.965895i	$-0.416628\pi$
$499$	11.5684	0.517871	0.258936	+	0.965895i	$0.416628\pi$
$500$	−24.4751	−1.09456
$501$	−51.7756	−2.31316
$502$	18.0464	0.805451
$503$	8.03393	0.358215	0.179108	−	0.983830i	$-0.442679\pi$
$503$	8.03393	0.358215	0.179108	+	0.983830i	$0.442679\pi$
$504$	−4.30516	−0.191767
$505$	2.21402	0.0985226
$506$	−5.51177	−0.245028
$507$	25.8229	1.14684
$508$	−17.9486	−0.796339
$509$	22.2088	0.984390	0.492195	−	0.870485i	$-0.336195\pi$
$509$	22.2088	0.984390	0.492195	+	0.870485i	$0.336195\pi$
$510$	−14.0127	−0.620492
$511$	1.78333	0.0788897
$512$	1.00000	0.0441942
$513$	13.6732	0.603689
$514$	−23.2017	−1.02338
$515$	−4.83975	−0.213265
$516$	16.5113	0.726871
$517$	−7.84932	−0.345213
$518$	21.7112	0.953936
$519$	−19.1584	−0.840963
$520$	−2.61953	−0.114874
$521$	14.4049	0.631089	0.315544	−	0.948911i	$-0.397813\pi$
$521$	14.4049	0.631089	0.315544	+	0.948911i	$0.397813\pi$
$522$	1.21772	0.0532982
$523$	−4.95589	−0.216706	−0.108353	−	0.994112i	$-0.534558\pi$
$523$	−4.95589	−0.216706	−0.108353	+	0.994112i	$0.534558\pi$
$524$	−12.9396	−0.565271
$525$	80.5926	3.51735
$526$	7.85841	0.342643
$527$	−17.1116	−0.745394
$528$	11.3196	0.492621
$529$	1.00000	0.0434783
$530$	53.9939	2.34534
$531$	12.9262	0.560950
$532$	−13.2068	−0.572589
$533$	−7.44401	−0.322436
$534$	−24.3588	−1.05411
$535$	−7.52678	−0.325411
$536$	6.39521	0.276231
$537$	−33.3315	−1.43836
$538$	−0.813498	−0.0350724
$539$	−30.3105	−1.30557
$540$	−14.6867	−0.632016
$541$	7.95254	0.341906	0.170953	−	0.985279i	$-0.445315\pi$
$541$	7.95254	0.341906	0.170953	+	0.985279i	$0.445315\pi$
$542$	22.4466	0.964166
$543$	29.1095	1.24921
$544$	−1.70048	−0.0729076
$545$	−39.0538	−1.67288
$546$	4.74017	0.202860
$547$	4.63455	0.198159	0.0990796	−	0.995080i	$-0.468410\pi$
$547$	4.63455	0.198159	0.0990796	+	0.995080i	$0.468410\pi$
$548$	7.26481	0.310337
$549$	−1.84567	−0.0787715
$550$	−61.1795	−2.60870
$551$	3.73557	0.159141
$552$	−2.05371	−0.0874117
$553$	−22.0526	−0.937771
$554$	12.6782	0.538645
$555$	−50.6048	−2.14805
$556$	−5.41103	−0.229479
$557$	−0.344060	−0.0145783	−0.00728914	−	0.999973i	$-0.502320\pi$
$557$	−0.344060	−0.0145783	−0.00728914	+	0.999973i	$0.502320\pi$
$558$	12.2537	0.518739
$559$	−5.24876	−0.221999
$560$	14.1857	0.599456
$561$	−19.2487	−0.812683
$562$	16.9169	0.713598
$563$	17.1221	0.721609	0.360804	−	0.932642i	$-0.382502\pi$
$563$	17.1221	0.721609	0.360804	+	0.932642i	$0.382502\pi$
$564$	−2.92469	−0.123152
$565$	−45.0042	−1.89334
$566$	31.0461	1.30496
$567$	39.4918	1.65850
$568$	−5.18060	−0.217373
$569$	7.09450	0.297417	0.148709	−	0.988881i	$-0.452488\pi$
$569$	7.09450	0.297417	0.148709	+	0.988881i	$0.452488\pi$
$570$	30.7826	1.28934
$571$	28.5912	1.19650	0.598251	−	0.801308i	$-0.295862\pi$
$571$	28.5912	1.19650	0.598251	+	0.801308i	$0.295862\pi$
$572$	−3.59836	−0.150455
$573$	−52.6566	−2.19976
$574$	40.3121	1.68259
$575$	11.0998	0.462893
$576$	1.21772	0.0507383
$577$	−35.2631	−1.46802	−0.734012	−	0.679137i	$-0.762354\pi$
$577$	−35.2631	−1.46802	−0.734012	+	0.679137i	$0.762354\pi$
$578$	−14.1084	−0.586830
$579$	−23.9458	−0.995155
$580$	−4.01245	−0.166608
$581$	−0.795368	−0.0329974
$582$	−12.3472	−0.511808
$583$	74.1696	3.07179
$584$	−0.504417	−0.0208729
$585$	−3.18985	−0.131884
$586$	0.204091	0.00843090
$587$	36.9879	1.52665	0.763327	−	0.646013i	$-0.223565\pi$
$587$	36.9879	1.52665	0.763327	+	0.646013i	$0.223565\pi$
$588$	−11.2938	−0.465749
$589$	37.5903	1.54888
$590$	−42.5926	−1.75351
$591$	19.8171	0.815166
$592$	−6.14105	−0.252396
$593$	−12.8082	−0.525969	−0.262985	−	0.964800i	$-0.584707\pi$
$593$	−12.8082	−0.525969	−0.262985	+	0.964800i	$0.584707\pi$
$594$	−20.1747	−0.827776
$595$	−24.1226	−0.988930
$596$	−16.2539	−0.665788
$597$	3.47599	0.142263
$598$	0.652850	0.0266970
$599$	−28.8605	−1.17921	−0.589603	−	0.807693i	$-0.700716\pi$
$599$	−28.8605	−1.17921	−0.589603	+	0.807693i	$0.700716\pi$
$600$	−22.7957	−0.930632
$601$	11.5088	0.469454	0.234727	−	0.972061i	$-0.424580\pi$
$601$	11.5088	0.469454	0.234727	+	0.972061i	$0.424580\pi$
$602$	28.4240	1.15848
$603$	7.78758	0.317135
$604$	8.56052	0.348323
$605$	−77.7600	−3.16139
$606$	1.13321	0.0460335
$607$	−34.1328	−1.38541	−0.692703	−	0.721223i	$-0.743580\pi$
$607$	−34.1328	−1.38541	−0.692703	+	0.721223i	$0.743580\pi$
$608$	3.73557	0.151497
$609$	7.26073	0.294220
$610$	6.08160	0.246237
$611$	0.929724	0.0376126
$612$	−2.07071	−0.0837036
$613$	38.3036	1.54707	0.773534	−	0.633755i	$-0.218487\pi$
$613$	38.3036	1.54707	0.773534	+	0.633755i	$0.218487\pi$
$614$	−18.6866	−0.754129
$615$	−93.9599	−3.78883
$616$	19.4865	0.785132
$617$	1.08543	0.0436978	0.0218489	−	0.999761i	$-0.493045\pi$
$617$	1.08543	0.0436978	0.0218489	+	0.999761i	$0.493045\pi$
$618$	−2.47715	−0.0996455
$619$	16.6228	0.668125	0.334063	−	0.942551i	$-0.391580\pi$
$619$	16.6228	0.668125	0.334063	+	0.942551i	$0.391580\pi$
$620$	−40.3765	−1.62156
$621$	3.66028	0.146882
$622$	−12.9694	−0.520027
$623$	−41.9332	−1.68002
$624$	−1.34076	−0.0536735
$625$	42.7063	1.70825
$626$	6.21956	0.248583
$627$	42.2851	1.68870
$628$	9.66034	0.385490
$629$	10.4427	0.416380
$630$	17.2742	0.688223
$631$	25.4604	1.01356	0.506782	−	0.862074i	$-0.330835\pi$
$631$	25.4604	1.01356	0.506782	+	0.862074i	$0.330835\pi$
$632$	6.23760	0.248118
$633$	−26.8167	−1.06587
$634$	2.43300	0.0966267
$635$	72.0178	2.85794
$636$	27.6359	1.09583
$637$	3.59017	0.142248
$638$	−5.51177	−0.218213
$639$	−6.30852	−0.249561
$640$	−4.01245	−0.158606
$641$	2.20026	0.0869052	0.0434526	−	0.999055i	$-0.486164\pi$
$641$	2.20026	0.0869052	0.0434526	+	0.999055i	$0.486164\pi$
$642$	−3.85246	−0.152044
$643$	−45.2399	−1.78409	−0.892044	−	0.451949i	$-0.850729\pi$
$643$	−45.2399	−1.78409	−0.892044	+	0.451949i	$0.850729\pi$
$644$	−3.53542	−0.139315
$645$	−66.2510	−2.60863
$646$	−6.35227	−0.249927
$647$	−29.4078	−1.15614	−0.578070	−	0.815988i	$-0.696194\pi$
$647$	−29.4078	−1.15614	−0.578070	+	0.815988i	$0.696194\pi$
$648$	−11.1703	−0.438812
$649$	−58.5080	−2.29664
$650$	7.24649	0.284231
$651$	73.0633	2.86358
$652$	−11.9648	−0.468577
$653$	−32.8248	−1.28453	−0.642267	−	0.766481i	$-0.722006\pi$
$653$	−32.8248	−1.28453	−0.642267	+	0.766481i	$0.722006\pi$
$654$	−19.9891	−0.781634
$655$	51.9197	2.02867
$656$	−11.4023	−0.445186
$657$	−0.614238	−0.0239637
$658$	−5.03480	−0.196277
$659$	7.64397	0.297767	0.148883	−	0.988855i	$-0.452432\pi$
$659$	7.64397	0.297767	0.148883	+	0.988855i	$0.452432\pi$
$660$	−45.4193	−1.76794
$661$	0.0824011	0.00320503	0.00160252	−	0.999999i	$-0.499490\pi$
$661$	0.0824011	0.00320503	0.00160252	+	0.999999i	$0.499490\pi$
$662$	3.43227	0.133399
$663$	2.27995	0.0885457
$664$	0.224971	0.00873057
$665$	52.9918	2.05493
$666$	−7.47808	−0.289770
$667$	1.00000	0.0387202
$668$	25.2108	0.975435
$669$	1.33542	0.0516303
$670$	−25.6605	−0.991351
$671$	8.35409	0.322506
$672$	7.26073	0.280089
$673$	−4.18403	−0.161282	−0.0806412	−	0.996743i	$-0.525697\pi$
$673$	−4.18403	−0.161282	−0.0806412	+	0.996743i	$0.525697\pi$
$674$	−26.7191	−1.02918
$675$	40.6284	1.56379
$676$	−12.5738	−0.483607
$677$	−38.5893	−1.48311	−0.741553	−	0.670895i	$-0.765910\pi$
$677$	−38.5893	−1.48311	−0.741553	+	0.670895i	$0.765910\pi$
$678$	−23.0347	−0.884641
$679$	−21.2555	−0.815711
$680$	6.82311	0.261654
$681$	2.53523	0.0971503
$682$	−55.4639	−2.12382
$683$	−19.5854	−0.749415	−0.374707	−	0.927143i	$-0.622257\pi$
$683$	−19.5854	−0.749415	−0.374707	+	0.927143i	$0.622257\pi$
$684$	4.54888	0.173931
$685$	−29.1497	−1.11375
$686$	5.30587	0.202579
$687$	29.7199	1.13388
$688$	−8.03976	−0.306513
$689$	−8.78512	−0.334687
$690$	8.24041	0.313707
$691$	28.4744	1.08322	0.541608	−	0.840631i	$-0.317816\pi$
$691$	28.4744	1.08322	0.541608	+	0.840631i	$0.317816\pi$
$692$	9.32871	0.354624
$693$	23.7291	0.901393
$694$	−8.08819	−0.307024
$695$	21.7115	0.823564
$696$	−2.05371	−0.0778456
$697$	19.3895	0.734428
$698$	19.0010	0.719198
$699$	57.1866	2.16300
$700$	−39.2425	−1.48323
$701$	25.3779	0.958511	0.479255	−	0.877675i	$-0.340907\pi$
$701$	25.3779	0.958511	0.479255	+	0.877675i	$0.340907\pi$
$702$	2.38962	0.0901902
$703$	−22.9403	−0.865210
$704$	−5.51177	−0.207733
$705$	11.7352	0.441972
$706$	25.7234	0.968115
$707$	1.95080	0.0733674
$708$	−21.8003	−0.819306
$709$	−27.4039	−1.02918	−0.514588	−	0.857438i	$-0.672055\pi$
$709$	−27.4039	−1.02918	−0.514588	+	0.857438i	$0.672055\pi$
$710$	20.7869	0.780119
$711$	7.59565	0.284859
$712$	11.8609	0.444505
$713$	10.0628	0.376855
$714$	−12.3468	−0.462066
$715$	14.4383	0.539960
$716$	16.2299	0.606540
$717$	21.8898	0.817490
$718$	−0.524332	−0.0195679
$719$	39.3867	1.46888	0.734438	−	0.678676i	$-0.237446\pi$
$719$	39.3867	1.46888	0.734438	+	0.678676i	$0.237446\pi$
$720$	−4.88605	−0.182092
$721$	−4.26437	−0.158813
$722$	−5.04552	−0.187775
$723$	−43.2120	−1.60707
$724$	−14.1741	−0.526777
$725$	11.0998	0.412236
$726$	−39.8002	−1.47712
$727$	−46.4746	−1.72365	−0.861823	−	0.507208i	$-0.830677\pi$
$727$	−46.4746	−1.72365	−0.861823	+	0.507208i	$0.830677\pi$
$728$	−2.30810	−0.0855439
$729$	8.94915	0.331450
$730$	2.02395	0.0749097
$731$	13.6715	0.505658
$732$	3.11277	0.115051
$733$	−12.6986	−0.469033	−0.234516	−	0.972112i	$-0.575351\pi$
$733$	−12.6986	−0.469033	−0.234516	+	0.972112i	$0.575351\pi$
$734$	30.2026	1.11480
$735$	45.3159	1.67150
$736$	1.00000	0.0368605
$737$	−35.2490	−1.29841
$738$	−13.8848	−0.511108
$739$	−6.61050	−0.243171	−0.121586	−	0.992581i	$-0.538798\pi$
$739$	−6.61050	−0.243171	−0.121586	+	0.992581i	$0.538798\pi$
$740$	24.6407	0.905809
$741$	−5.00852	−0.183992
$742$	47.5747	1.74652
$743$	30.9254	1.13454	0.567272	−	0.823531i	$-0.307999\pi$
$743$	30.9254	1.13454	0.567272	+	0.823531i	$0.307999\pi$
$744$	−20.6661	−0.757654
$745$	65.2182	2.38941
$746$	−13.8974	−0.508821
$747$	0.273952	0.0100234
$748$	9.37268	0.342699
$749$	−6.63194	−0.242326
$750$	50.2647	1.83541
$751$	20.9349	0.763925	0.381962	−	0.924178i	$-0.375248\pi$
$751$	20.9349	0.763925	0.381962	+	0.924178i	$0.375248\pi$
$752$	1.42410	0.0519316
$753$	−37.0621	−1.35062
$754$	0.652850	0.0237754
$755$	−34.3487	−1.25008
$756$	−12.9407	−0.470647
$757$	23.3625	0.849124	0.424562	−	0.905399i	$-0.360428\pi$
$757$	23.3625	0.849124	0.424562	+	0.905399i	$0.360428\pi$
$758$	−6.36361	−0.231137
$759$	11.3196	0.410875
$760$	−14.9888	−0.543701
$761$	16.0870	0.583152	0.291576	−	0.956548i	$-0.405820\pi$
$761$	16.0870	0.583152	0.291576	+	0.956548i	$0.405820\pi$
$762$	36.8612	1.33534
$763$	−34.4108	−1.24576
$764$	25.6398	0.927614
$765$	8.30864	0.300399
$766$	−1.24342	−0.0449267
$767$	6.93006	0.250230
$768$	−2.05371	−0.0741068
$769$	−7.86314	−0.283552	−0.141776	−	0.989899i	$-0.545281\pi$
$769$	−7.86314	−0.283552	−0.141776	+	0.989899i	$0.545281\pi$
$770$	−78.1885	−2.81772
$771$	47.6496	1.71606
$772$	11.6598	0.419645
$773$	−12.8613	−0.462590	−0.231295	−	0.972884i	$-0.574296\pi$
$773$	−12.8613	−0.462590	−0.231295	+	0.972884i	$0.574296\pi$
$774$	−9.79019	−0.351901
$775$	111.695	4.01220
$776$	6.01214	0.215823
$777$	−44.5885	−1.59960
$778$	−21.6016	−0.774455
$779$	−42.5942	−1.52609
$780$	5.37975	0.192626
$781$	28.5543	1.02175
$782$	−1.70048	−0.0608091
$783$	3.66028	0.130808
$784$	5.49923	0.196401
$785$	−38.7617	−1.38346
$786$	26.5743	0.947872
$787$	12.3333	0.439633	0.219816	−	0.975541i	$-0.429454\pi$
$787$	12.3333	0.439633	0.219816	+	0.975541i	$0.429454\pi$
$788$	−9.64941	−0.343746
$789$	−16.1389	−0.574559
$790$	−25.0281	−0.890459
$791$	−39.6538	−1.40993
$792$	−6.71180	−0.238493
$793$	−0.989512	−0.0351386
$794$	−32.1432	−1.14072
$795$	−110.888	−3.93278
$796$	−1.69254	−0.0599907
$797$	−17.8376	−0.631841	−0.315921	−	0.948786i	$-0.602313\pi$
$797$	−17.8376	−0.631841	−0.315921	+	0.948786i	$0.602313\pi$
$798$	27.1230	0.960143
$799$	−2.42166	−0.0856721
$800$	11.0998	0.392437
$801$	14.4432	0.510326
$802$	−7.66396	−0.270624
$803$	2.78023	0.0981122
$804$	−13.1339	−0.463197
$805$	14.1857	0.499981
$806$	6.56950	0.231401
$807$	1.67069	0.0588110
$808$	−0.551787	−0.0194118
$809$	18.0382	0.634188	0.317094	−	0.948394i	$-0.397293\pi$
$809$	18.0382	0.634188	0.317094	+	0.948394i	$0.397293\pi$
$810$	44.8204	1.57483
$811$	49.5953	1.74153	0.870763	−	0.491703i	$-0.163625\pi$
$811$	49.5953	1.74153	0.870763	+	0.491703i	$0.163625\pi$
$812$	−3.53542	−0.124069
$813$	−46.0989	−1.61676
$814$	33.8481	1.18637
$815$	48.0082	1.68165
$816$	3.49230	0.122255
$817$	−30.0331	−1.05073
$818$	39.2906	1.37376
$819$	−2.81062	−0.0982111
$820$	45.7513	1.59770
$821$	8.95961	0.312693	0.156346	−	0.987702i	$-0.450028\pi$
$821$	8.95961	0.312693	0.156346	+	0.987702i	$0.450028\pi$
$822$	−14.9198	−0.520388
$823$	11.8980	0.414740	0.207370	−	0.978263i	$-0.433510\pi$
$823$	11.8980	0.414740	0.207370	+	0.978263i	$0.433510\pi$
$824$	1.20618	0.0420193
$825$	125.645	4.37439
$826$	−37.5289	−1.30580
$827$	−29.9652	−1.04199	−0.520996	−	0.853559i	$-0.674439\pi$
$827$	−29.9652	−1.04199	−0.520996	+	0.853559i	$0.674439\pi$
$828$	1.21772	0.0423187
$829$	29.4996	1.02456	0.512282	−	0.858817i	$-0.328800\pi$
$829$	29.4996	1.02456	0.512282	+	0.858817i	$0.328800\pi$
$830$	−0.902686	−0.0313327
$831$	−26.0373	−0.903225
$832$	0.652850	0.0226335
$833$	−9.35134	−0.324005
$834$	11.1127	0.384801
$835$	−101.157	−3.50069
$836$	−20.5896	−0.712107
$837$	36.8327	1.27312
$838$	12.9800	0.448386
$839$	−35.0057	−1.20853	−0.604265	−	0.796783i	$-0.706533\pi$
$839$	−35.0057	−1.20853	−0.604265	+	0.796783i	$0.706533\pi$
$840$	−29.1334	−1.00520
$841$	1.00000	0.0344828
$842$	−1.36101	−0.0469033
$843$	−34.7425	−1.19659
$844$	13.0577	0.449464
$845$	50.4517	1.73559
$846$	1.73416	0.0596215
$847$	−68.5153	−2.35421
$848$	−13.4566	−0.462101
$849$	−63.7596	−2.18822
$850$	−18.8750	−0.647407
$851$	−6.14105	−0.210512
$852$	10.6394	0.364501
$853$	−23.4809	−0.803971	−0.401986	−	0.915646i	$-0.631680\pi$
$853$	−23.4809	−0.803971	−0.401986	+	0.915646i	$0.631680\pi$
$854$	5.35857	0.183367
$855$	−18.2522	−0.624211
$856$	1.87585	0.0641154
$857$	−3.69994	−0.126387	−0.0631937	−	0.998001i	$-0.520129\pi$
$857$	−3.69994	−0.126387	−0.0631937	+	0.998001i	$0.520129\pi$
$858$	7.38999	0.252290
$859$	−46.9693	−1.60257	−0.801286	−	0.598281i	$-0.795851\pi$
$859$	−46.9693	−1.60257	−0.801286	+	0.598281i	$0.795851\pi$
$860$	32.2592	1.10003
$861$	−82.7892	−2.82145
$862$	14.9961	0.510768
$863$	5.79985	0.197429	0.0987146	−	0.995116i	$-0.468527\pi$
$863$	5.79985	0.197429	0.0987146	+	0.995116i	$0.468527\pi$
$864$	3.66028	0.124525
$865$	−37.4310	−1.27269
$866$	35.9301	1.22095
$867$	28.9745	0.984024
$868$	−35.5763	−1.20754
$869$	−34.3802	−1.16627
$870$	8.24041	0.279376
$871$	4.17511	0.141468
$872$	9.73315	0.329606
$873$	7.32111	0.247782
$874$	3.73557	0.126358
$875$	86.5299	2.92524
$876$	1.03592	0.0350007
$877$	37.5505	1.26799	0.633994	−	0.773338i	$-0.281414\pi$
$877$	37.5505	1.26799	0.633994	+	0.773338i	$0.281414\pi$
$878$	−8.90014	−0.300365
$879$	−0.419143	−0.0141373
$880$	22.1157	0.745521
$881$	49.8042	1.67795	0.838973	−	0.544174i	$-0.183157\pi$
$881$	49.8042	1.67795	0.838973	+	0.544174i	$0.183157\pi$
$882$	6.69652	0.225484
$883$	−35.8882	−1.20773	−0.603867	−	0.797085i	$-0.706374\pi$
$883$	−35.8882	−1.20773	−0.603867	+	0.797085i	$0.706374\pi$
$884$	−1.11016	−0.0373387
$885$	87.4727	2.94036
$886$	2.51759	0.0845800
$887$	−15.5155	−0.520960	−0.260480	−	0.965479i	$-0.583881\pi$
$887$	−15.5155	−0.520960	−0.260480	+	0.965479i	$0.583881\pi$
$888$	12.6119	0.423229
$889$	63.4558	2.12824
$890$	−47.5912	−1.59526
$891$	61.5683	2.06261
$892$	−0.650247	−0.0217719
$893$	5.31983	0.178021
$894$	33.3809	1.11642
$895$	−65.1218	−2.17678
$896$	−3.53542	−0.118110
$897$	−1.34076	−0.0447668
$898$	31.2412	1.04253
$899$	10.0628	0.335613
$900$	13.5164	0.450548
$901$	22.8827	0.762332
$902$	62.8470	2.09258
$903$	−58.3746	−1.94258
$904$	11.2161	0.373043
$905$	56.8730	1.89052
$906$	−17.5808	−0.584083
$907$	41.9224	1.39201	0.696005	−	0.718037i	$-0.254959\pi$
$907$	41.9224	1.39201	0.696005	+	0.718037i	$0.254959\pi$
$908$	−1.23447	−0.0409672
$909$	−0.671922	−0.0222862
$910$	9.26115	0.307004
$911$	−26.6176	−0.881881	−0.440941	−	0.897536i	$-0.645355\pi$
$911$	−26.6176	−0.881881	−0.440941	+	0.897536i	$0.645355\pi$
$912$	−7.67177	−0.254038
$913$	−1.23999	−0.0410377
$914$	38.7886	1.28301
$915$	−12.4898	−0.412901
$916$	−14.4713	−0.478146
$917$	45.7471	1.51070
$918$	−6.22425	−0.205431
$919$	27.6069	0.910667	0.455333	−	0.890321i	$-0.349520\pi$
$919$	27.6069	0.910667	0.455333	+	0.890321i	$0.349520\pi$
$920$	−4.01245	−0.132287
$921$	38.3768	1.26456
$922$	−24.5073	−0.807106
$923$	−3.38215	−0.111325
$924$	−40.0195	−1.31655
$925$	−68.1643	−2.24123
$926$	−39.1005	−1.28492
$927$	1.46879	0.0482415
$928$	1.00000	0.0328266
$929$	41.7223	1.36886	0.684432	−	0.729077i	$-0.260050\pi$
$929$	41.7223	1.36886	0.684432	+	0.729077i	$0.260050\pi$
$930$	82.9216	2.71911
$931$	20.5428	0.673261
$932$	−27.8455	−0.912110
$933$	26.6355	0.872006
$934$	−18.9638	−0.620514
$935$	−37.6074	−1.22989
$936$	0.794989	0.0259850
$937$	−31.9301	−1.04311	−0.521556	−	0.853217i	$-0.674648\pi$
$937$	−31.9301	−1.04311	−0.521556	+	0.853217i	$0.674648\pi$
$938$	−22.6098	−0.738236
$939$	−12.7732	−0.416836
$940$	−5.71414	−0.186375
$941$	26.6179	0.867718	0.433859	−	0.900981i	$-0.357152\pi$
$941$	26.6179	0.867718	0.433859	+	0.900981i	$0.357152\pi$
$942$	−19.8395	−0.646407
$943$	−11.4023	−0.371311
$944$	10.6151	0.345492
$945$	51.9238	1.68908
$946$	44.3134	1.44075
$947$	−6.97578	−0.226682	−0.113341	−	0.993556i	$-0.536155\pi$
$947$	−6.97578	−0.226682	−0.113341	+	0.993556i	$0.536155\pi$
$948$	−12.8102	−0.416056
$949$	−0.329308	−0.0106898
$950$	41.4640	1.34527
$951$	−4.99667	−0.162028
$952$	6.01193	0.194848
$953$	−5.01663	−0.162504	−0.0812522	−	0.996694i	$-0.525892\pi$
$953$	−5.01663	−0.162504	−0.0812522	+	0.996694i	$0.525892\pi$
$954$	−16.3863	−0.530528
$955$	−102.878	−3.32906
$956$	−10.6587	−0.344726
$957$	11.3196	0.365910
$958$	2.26922	0.0733153
$959$	−25.6842	−0.829386
$960$	8.24041	0.265958
$961$	70.2599	2.26645
$962$	−4.00918	−0.129261
$963$	2.28427	0.0736095
$964$	21.0409	0.677683
$965$	−46.7844	−1.50604
$966$	7.26073	0.233610
$967$	−5.76948	−0.185534	−0.0927669	−	0.995688i	$-0.529571\pi$
$967$	−5.76948	−0.185534	−0.0927669	+	0.995688i	$0.529571\pi$
$968$	19.3797	0.622886
$969$	13.0457	0.419089
$970$	−24.1235	−0.774557
$971$	24.6935	0.792453	0.396227	−	0.918153i	$-0.370319\pi$
$971$	24.6935	0.792453	0.396227	+	0.918153i	$0.370319\pi$
$972$	11.9597	0.383609
$973$	19.1303	0.613289
$974$	−32.2461	−1.03323
$975$	−14.8822	−0.476611
$976$	−1.51568	−0.0485157
$977$	−5.21955	−0.166988	−0.0834940	−	0.996508i	$-0.526608\pi$
$977$	−5.21955	−0.166988	−0.0834940	+	0.996508i	$0.526608\pi$
$978$	24.5722	0.785732
$979$	−65.3744	−2.08938
$980$	−22.0654	−0.704853
$981$	11.8523	0.378414
$982$	23.7963	0.759372
$983$	−33.5367	−1.06965	−0.534827	−	0.844961i	$-0.679623\pi$
$983$	−33.5367	−1.06965	−0.534827	+	0.844961i	$0.679623\pi$
$984$	23.4171	0.746508
$985$	38.7178	1.23365
$986$	−1.70048	−0.0541544
$987$	10.3400	0.329126
$988$	2.43877	0.0775875
$989$	−8.03976	−0.255650
$990$	26.9308	0.855916
$991$	−44.3078	−1.40748	−0.703742	−	0.710455i	$-0.748489\pi$
$991$	−44.3078	−1.40748	−0.703742	+	0.710455i	$0.748489\pi$
$992$	10.0628	0.319494
$993$	−7.04889	−0.223690
$994$	18.3156	0.580936
$995$	6.79126	0.215297
$996$	−0.462025	−0.0146398
$997$	−2.48868	−0.0788172	−0.0394086	−	0.999223i	$-0.512547\pi$
$997$	−2.48868	−0.0788172	−0.0394086	+	0.999223i	$0.512547\pi$
$998$	11.5684	0.366190
$999$	−22.4780	−0.711172

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.k.1.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.k.1.2	✓	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.05371 q^{3} +1.00000 q^{4} -4.01245 q^{5} -2.05371 q^{6} -3.53542 q^{7} +1.00000 q^{8} +1.21772 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.05371 q^{3} +1.00000 q^{4} -4.01245 q^{5} -2.05371 q^{6} -3.53542 q^{7} +1.00000 q^{8} +1.21772 q^{9} -4.01245 q^{10} -5.51177 q^{11} -2.05371 q^{12} +0.652850 q^{13} -3.53542 q^{14} +8.24041 q^{15} +1.00000 q^{16} -1.70048 q^{17} +1.21772 q^{18} +3.73557 q^{19} -4.01245 q^{20} +7.26073 q^{21} -5.51177 q^{22} +1.00000 q^{23} -2.05371 q^{24} +11.0998 q^{25} +0.652850 q^{26} +3.66028 q^{27} -3.53542 q^{28} +1.00000 q^{29} +8.24041 q^{30} +10.0628 q^{31} +1.00000 q^{32} +11.3196 q^{33} -1.70048 q^{34} +14.1857 q^{35} +1.21772 q^{36} -6.14105 q^{37} +3.73557 q^{38} -1.34076 q^{39} -4.01245 q^{40} -11.4023 q^{41} +7.26073 q^{42} -8.03976 q^{43} -5.51177 q^{44} -4.88605 q^{45} +1.00000 q^{46} +1.42410 q^{47} -2.05371 q^{48} +5.49923 q^{49} +11.0998 q^{50} +3.49230 q^{51} +0.652850 q^{52} -13.4566 q^{53} +3.66028 q^{54} +22.1157 q^{55} -3.53542 q^{56} -7.67177 q^{57} +1.00000 q^{58} +10.6151 q^{59} +8.24041 q^{60} -1.51568 q^{61} +10.0628 q^{62} -4.30516 q^{63} +1.00000 q^{64} -2.61953 q^{65} +11.3196 q^{66} +6.39521 q^{67} -1.70048 q^{68} -2.05371 q^{69} +14.1857 q^{70} -5.18060 q^{71} +1.21772 q^{72} -0.504417 q^{73} -6.14105 q^{74} -22.7957 q^{75} +3.73557 q^{76} +19.4865 q^{77} -1.34076 q^{78} +6.23760 q^{79} -4.01245 q^{80} -11.1703 q^{81} -11.4023 q^{82} +0.224971 q^{83} +7.26073 q^{84} +6.82311 q^{85} -8.03976 q^{86} -2.05371 q^{87} -5.51177 q^{88} +11.8609 q^{89} -4.88605 q^{90} -2.30810 q^{91} +1.00000 q^{92} -20.6661 q^{93} +1.42410 q^{94} -14.9888 q^{95} -2.05371 q^{96} +6.01214 q^{97} +5.49923 q^{98} -6.71180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9} - q^{10} + q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 10 q^{16} + 11 q^{18} + 20 q^{19} - q^{20} + 14 q^{21} + q^{22} + 10 q^{23} + 5 q^{24} + 23 q^{25} + 9 q^{26} + 23 q^{27} + 2 q^{28} + 10 q^{29} + 5 q^{30} + 21 q^{31} + 10 q^{32} + q^{33} + 2 q^{35} + 11 q^{36} - 8 q^{37} + 20 q^{38} + 23 q^{39} - q^{40} - 4 q^{41} + 14 q^{42} - 3 q^{43} + q^{44} - 18 q^{45} + 10 q^{46} - q^{47} + 5 q^{48} + 18 q^{49} + 23 q^{50} - 6 q^{51} + 9 q^{52} - 13 q^{53} + 23 q^{54} + 13 q^{55} + 2 q^{56} - 22 q^{57} + 10 q^{58} + 14 q^{59} + 5 q^{60} + 12 q^{61} + 21 q^{62} - 26 q^{63} + 10 q^{64} - 25 q^{65} + q^{66} + 6 q^{67} + 5 q^{69} + 2 q^{70} + 8 q^{71} + 11 q^{72} + 16 q^{73} - 8 q^{74} + 8 q^{75} + 20 q^{76} - 16 q^{77} + 23 q^{78} + 7 q^{79} - q^{80} - 2 q^{81} - 4 q^{82} + 18 q^{83} + 14 q^{84} + 8 q^{85} - 3 q^{86} + 5 q^{87} + q^{88} + 2 q^{89} - 18 q^{90} + 8 q^{91} + 10 q^{92} - 41 q^{93} - q^{94} - 16 q^{95} + 5 q^{96} + 6 q^{97} + 18 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9 - q^10 + q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 10 * q^16 + 11 * q^18 + 20 * q^19 - q^20 + 14 * q^21 + q^22 + 10 * q^23 + 5 * q^24 + 23 * q^25 + 9 * q^26 + 23 * q^27 + 2 * q^28 + 10 * q^29 + 5 * q^30 + 21 * q^31 + 10 * q^32 + q^33 + 2 * q^35 + 11 * q^36 - 8 * q^37 + 20 * q^38 + 23 * q^39 - q^40 - 4 * q^41 + 14 * q^42 - 3 * q^43 + q^44 - 18 * q^45 + 10 * q^46 - q^47 + 5 * q^48 + 18 * q^49 + 23 * q^50 - 6 * q^51 + 9 * q^52 - 13 * q^53 + 23 * q^54 + 13 * q^55 + 2 * q^56 - 22 * q^57 + 10 * q^58 + 14 * q^59 + 5 * q^60 + 12 * q^61 + 21 * q^62 - 26 * q^63 + 10 * q^64 - 25 * q^65 + q^66 + 6 * q^67 + 5 * q^69 + 2 * q^70 + 8 * q^71 + 11 * q^72 + 16 * q^73 - 8 * q^74 + 8 * q^75 + 20 * q^76 - 16 * q^77 + 23 * q^78 + 7 * q^79 - q^80 - 2 * q^81 - 4 * q^82 + 18 * q^83 + 14 * q^84 + 8 * q^85 - 3 * q^86 + 5 * q^87 + q^88 + 2 * q^89 - 18 * q^90 + 8 * q^91 + 10 * q^92 - 41 * q^93 - q^94 - 16 * q^95 + 5 * q^96 + 6 * q^97 + 18 * q^98 - 22 * q^99

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